Towards a Normal Form for Extended Relations Defined by Regular Expressions

Abstract

XML elements are described by XML schema languages such as a DTD or an XML Schema definition. The instances of these elements are semi-structured tuples. We may think of a semi-structure tuple as a sentence of a formal language, where the values are the terminal symbols and the attribute names are the nonterminal symbols. In our former work [13] we introduced the notion of the extended tuple as a sentence from a regular language generated by a grammar where the nonterminal symbols of the grammar are the attribute names of the tuple. Sets of extended tuples are the extended relations. We then introduced the dual language, which generates the tuple types allowed to occur in extended relations. We defined functional dependencies (regular FD - RFD) over extended relations. In this paper we rephrase the RFD concept by directly using regular expressions over attribute names to define extended tuples. By the help of a special vertex labeled graph associated to regular expressions the specification of substring selection for the projection operation can be defined. The normalization for regular schemas is more complex than it is in the relational model, because the schema of an extended relation can contain an infinite number of tuple types. However, we can define selection, projection and join operations on extended relations too, so a lossless-join decomposition can be performed.